Operational Impedance Matrices of n-Phase Partially Symmetrical Machines

Abstract

By an affine transformation of space with origin fixed, the hyper-space associated with an n-phase partially-symmetrical machine having multi-winding in the field system is partitioned into two orthogonal sub-spaces of n-2 and 2 dimensions respectively. The armature reaction and the saliency effect of the machine are found to depend only upon the interaction of two rotating axes on the 2-dimensional plane. The complex stationary axes in the n-2 dimensional sub-space do not react on the field system and hence are named the zero armature-reaction axes. This supports a conclusion that, barring single-phase machines, the transient and steady-state performance characteristics of machines of any number of phases under balanced load conditions are essentially the same. For transient solutions, the cases of suddenly-applied voltages and sudden short- circuits are considered. The correlation between the machine parameters as obtained in the present analysis with those obtained by the two-reaction method is established.